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Sabtu, 07 Agustus 2010

Wave Function Properties

Transverse wave is a wave that has a propagation direction perpendicular to the direction of vibration. Examples of transverse waves are waves on a string. Wave vibration direction is vertical, while rambatnva horizontal direction so that direction and the direction of vibration satins rambatnva

A. Understanding Waves:

Is a form of vibration waves that propagate in a medium. In a tuner occure rather than substance intermediary medium. One wave length can be seen by calculating the distance between the valleys and hills (analyze the transversal wave) or the distance between a density menhitung with one renggangan (longitudinal wave). Fast wave propagation is the distance traveled by a wave in one second.

B. Types of Waves:

1. Transverse wave

Transverse waves are waves which direction perpendicular to the direction rambatannya rambatannya. A wave consists of a valley and a hill, such as wavelength of water, which vibrated yarn, etc..

Transverse wave

A wave can be grouped into trasnversal wave if the particles of the medium vibrate upwards and downwards in the direction perpendicular to the wave motion. Examples of transverse waves are waves of string. When we move the rope up and down, it appears that the rope moves up and down in the direction perpendicular to the direction of wave motion. Transverse wave form look like the picture below.

Based on the picture above, it appears that the waves propagate to the right in the horizontal plane, while the vibration direction up and down in a vertical plane. The dotted lines drawn in the middle along the direction of wave propagation state equilibrium position of the medium (eg a rope or water). The highest point is called the wave peak, while the lowest point is called the valley. Peak amplitude is the maximum height or maximum depth of the valley, measured from the equilibrium position. The distance of two equal and consecutive points on a wave is called wavelength (called lambda - greek letters). Wavelengths can also be also considered as the distance from peak to peak or from valley to valley distance.Vibration wave is propagating. In the propagation is not followed by the transfer of intermediate particles. At the bottom wave is the propagation of energy (vibrational energy)

Wave typesAccording to the vibration direction:- Transverse wave is the wave vibration direction perpendicular to the direction rambatannya. Examples: waves on a string, water waves, light gelobang, dll.jadi, water surface waves including transverse wave, since the wave vibration direction perpendicular to the direction rambatannya ...A transverse wave is moving waves of oscillation occurs perpendicular to the direction of energy transfer. If a transverse wave is moving in the positive x-direction, its oscillations are in up and down directions That lie in the y-z plane. If a transverse wave move in the positive x-direction, oscillating above and downward direction lies in the field of Zy.

If you anchor one end of a ribbon or string and hold the other end in your hand, Can you create transverse waves by moving your hand up-and-down menus. If you anchor one end of ribbon or string and hold the other end in your hand, you can create a transverse wave by moving your hand up and down. Notice though, that you Can Also launched waves by moving your hand side-to-side. Note also, that you can also start the wave by moving your hands to the sides. This is an Important point. This is an important point. There are two independent directions in Which wave motion cans occur. There are two independent directions in which wave motion can occur. In this case, These are the y and z directions mentioned above. In this case, this is y and z directions mentioned above. Further, if you carefully move your hand in a clockwise circle, you will from launch waves That DESCRIBE a left-Handed helix propagate away as they want. Furthermore, if you carefully move your hands in a circle clockwise, you will start left-handed helical waves that describe when they spread out. Similarly, if you move your hand in a counter-clockwise circle, a Right-Handed helix will of the form. Similarly, if you move your hands in a circle counter-clockwise, a right hand helix will be formed. These phenomena of simultaneous motion in two directions to go beyond the kinds of waves Can you create on-the surface of water; in general a wave on a string Can be two-dimensional. This phenomenon is simultaneous movement in two directions beyond the type of waves you can make on the surface of the water, generally the waves on a string can be two-dimensional. Two-dimensional transverse waves exhibit a Phenomenon Called Polarization. -Two-dimensional transverse wave shows that the phenomenon is called polarization. A wave Produced by moving your hand in a line, up and down for instance, is a linearly polarized wave, a special case. Waves generated by moving your hands in a row, top and bottom for example, is a linear polarized wave, a special case. A wave Produced by moving your hand in a circle is a circularly polarized wave, another special case. Waves generated by moving your hands in a circle is a circularly polarized wave, one special case. If your motion is not strictly in a line or a circle of your hand will from DESCRIBE of the Ellipse and the will of some elliptically polarized wave. If your motion is not strictly in line or circle your hand will describe an ellipse and the wave will be elliptically polarized.

Electromagnetic waves behave in this Same way, although it is harder to see. electromagnetic waves behave in a similar manner, although more difficult to see. Also electromagnetic waves are transverse two-dimensional waves. Electromagnetic waves are also two-dimensional transverse wave.

Ray theory does not DESCRIBE phenomena Poor 'Interference and Diffraction, Which Require wave theory (involving the phase of the wave). Ray theory does not describe phenomena such as interference and diffraction, which requires the wave theory (involving the phase of the wave). Can you think of a ray of light, in optics, as an idealized narrow beam of electromagnetic radiation. You can think of a ray of light, optics, as an ideal narrow beam of electromagnetic radiation. Rays Are Used to model the propagation of light through an optical system, by Dividing the real light field up into discrete rays That Can be computationally propagated through the system by the techniques of ray tracing. [1] A light ray is a line or curve That is perpendicular to the light's wavefronts (and is therefore collinear with the wave vector). Rays are used to model the propagation of light through an optical system, by dividing the field of real ray of light into discrete computing that can spread through the system with ray tracing techniques. [1] A ray of light is a line or curve that is perpendicular to the wave front of light (and therefore collinear with the wave vector). Light rays bend at the interface Between two dissimilar media Curved and May be in a medium in Which the refractive index changes. Light rays bend at the interface between two different media and can be curved in a medium where the refractive index changes. Geometrical optics describes how rays propagate through an optical system. [1] describes how the geometric optical rays propagating through optical systems. [1]

This two-dimensional nature Should not be confused with the two components of an electromagnetic wave, the electric and magnetic field components, Which are the electromagnetic wave shown in the diagram here. This two-dimensional nature is not to be confused with the two components of electromagnetic waves, electric and magnetic field components, shown in the diagram of electromagnetic waves here. The diagram shows a linear light wave Polarization. The diagram shows the linear polarization of light waves. Each of These fields, the electric and the magnetic, exhibits two-dimensional transverse wave behavior, just like the waves on a string. Each of these fields, and electrical, magnetic behavior shows a two-dimensional transverse waves, like waves on a string.

The transverse plane wave animation Also shown is an example of Linear Polarization. Plane transverse wave animation shown is also an example of linear polarization. The wave shown Could occur on a water surface. Waves shown in surface water can occur.

Transverse waves are waves That are moving perpendicular to the direction of vibration. Transverse waves are waves that move perpendicular to the direction of vibration.

Examples of transverse waves include seismic S (secondary) waves, and motion of electric (E) and magnetic (M) Field in the field of electromagnetic waves, both of which oscillate perpendicular to each other and the direction of energy transfer. Therefore an electromagnetic wave consists of two transverse waves, visible light being an example of an electromagnetic wave. Therefore, the electromagnetic wave comprises two transverse waves, visible light as an example of electromagnetic waves. See electromagnetic spectrum for information on Different types of electromagnetic waves. See electromagnetic spectrum for information on various types of electromagnetic waves.

An oscillating string is another example of a transverse wave; a more everyday example would be an audience wave. An oscillating string is another example of a transverse wave, an example of a more day-to-day will be the wave of the audience.

* Wave speed (v) - the speed of the wave's propagation speed of wave (v) - velocity of wave propagation * Amplitude (A) - the maximum magnitude of the displacement from equilibrium, in SI units of meters. amplitude (A) - the maximum amount of displacement from equilibrium, in SI units of meters. The amplitude is digit in blue in the picture. amplitudes are marked in blue in the picture. * Period (T) - is the time for one wave cycle (two pulses, or from crest to crest or trough to trough), in SI units of seconds (though it May be Referred to as "seconds per cycle"). period (T) - is the time for one wave cycle (two pulses, or from peak to peak or trough to trough), in SI units seconds (though it may be referred to as "cycles per second"). * Frequency (f) - the number of cycles in a unit of time. frequency (f) - the number of cycles in a single unit of time. The SI unit of frequncy is the hertz (Hz) and frequncy SI unit is the hertz (Hz) and

1 Hz = 1 cycle / s = 1 s -1 1 Hz = 1 cycle / s = 1 s -1

* Angular frequency (omega) - is 2pi times the frequency, in SI units of radians per second. angular frequency (omega) - is 2pi times the frequency, in SI units radians per second. * Wavelength (lambda) - The Distance Between any two points at corresponding positions on successive repetitions in the wave, so (for example) from one crest or trough to the next, in SI units of meters. wavelength (lambda) - the distance between two points on the relevant positions at consecutive repetition of the waves, so that (for example) from one peak or trough to the next, in SI units of meters. The wavelength is digit in red in the picture. Wavelength is shown in red in the picture. * Wave number (k) - Also Called the propagation constant, this useful quantity is defined as 2 pi divided by the wavelength, so the SI units are radians per meter. wave number (k) - also called the propagation constant, it's useful quantity is defined as 2 pi divided by the wavelength, so that SI units are radians per meter. * Pulse - one half-wavelength, pulse back from equilibrium - one half wavelength, the equilibrium return

Some useful equations in defining the above Quantities are: Some of the equations is useful in determining the amount of the above is:

v = lambda / T = Fy lambda = lambda / T = lambda f

omega = 2 pi f = 2 pi / T omega = 2 pi f = 2 pi / T

T = 1 / f = 2 pi / omega T = 1 / f = 2 pi / omega

k = 2 pi / omega k = 2 pi / omega

omega = omega = vK vK

The vertical position of a point on the wave, y, can be found as a function of the horizontal position, x, and the time, t, Pls We look at it. Vertical position of a point on the wave, y, can be found as a function of horizontal position, x, and time, t, when we see it. We thank the kind mathematicians for doing this work for us, and obtain the useful equations to DESCRIBE Following the wave motion: We thank the mathematician types to do this job for us, and obtain the following useful equation to describe wave motion:

The Wave Equation Wave EquationOne final feature of the wave function That is applying calculus to take the second derivative yields the wave equation, Which is an intriguing and useful Sometimes product (which, once again, We Will thank the mathematicians for and accept without proving it): One of the final feature of the wave function is that the calculus applies to take the second derivative wave equation, which is sometimes useful and interesting products (which, again, we would be grateful to the mathematicians to and accept without proving it):

The second derivative of y with respect to x is equivalent to the second derivative of y with respect to t divided by the wave speed squared. The second derivative of y with respect to x is equal to the second derivative of y with respect to t divided by the square of the wave velocity. The key usefulness of this equation is That Whenever it occurs, We Know That the function y acts as a wave with wave speed v and, therefore, the situation Can be described using the wave function. The main usefulness of this equation is that every time it happens, we know that y acts as a wave function with wave velocity v, and therefore, the situation can be described by using wave functions.

Sabtu, 31 Juli 2010

Wave Function Properties

Transverse wave is a wave that has a propagation direction perpendicular to the direction of vibration. Examples of transverse waves are waves on a string. Wave vibration direction is vertical, while rambatnva horizontal direction so that direction and the direction of vibration satins rambatnva

A. Understanding Waves:

Is a form of vibration waves that propagate in a medium. In a tuner occure rather than substance intermediary medium. One wave length can be seen by calculating the distance between the valleys and hills (analyze the transversal wave) or the distance between a density menhitung with one renggangan (longitudinal wave). Fast wave propagation is the distance traveled by a wave in one second.

B. Types of Waves:

1. Transverse wave

Transverse waves are waves which direction perpendicular to the direction rambatannya rambatannya. A wave consists of a valley and a hill, such as wavelength of water, which vibrated yarn, etc..

Transverse wave

A wave can be grouped into trasnversal wave if the particles of the medium vibrate upwards and downwards in the direction perpendicular to the wave motion. Examples of transverse waves are waves of string. When we move the rope up and down, it appears that the rope moves up and down in the direction perpendicular to the direction of wave motion. Transverse wave form look like the picture below.

Based on the picture above, it appears that the waves propagate to the right in the horizontal plane, while the vibration direction up and down in a vertical plane. The dotted lines drawn in the middle along the direction of wave propagation state equilibrium position of the medium (eg a rope or water). The highest point is called the wave peak, while the lowest point is called the valley. Peak amplitude is the maximum height or maximum depth of the valley, measured from the equilibrium position. The distance of two equal and consecutive points on a wave is called wavelength (called lambda - greek letters). Wavelengths can also be also considered as the distance from peak to peak or from valley to valley distance. Vibration wave is propagating. In the propagation is not followed by the transfer of intermediate particles. At the bottom wave is the propagation of energy (vibrational energy)

Wave types According to the vibration direction: - Transverse wave is the wave vibration direction perpendicular to the direction rambatannya. Examples: waves on a string, water waves, light gelobang, dll.jadi, water surface waves including transverse wave, since the wave vibration direction perpendicular to the direction rambatannya ... A transverse wave is moving waves of oscillation occurs perpendicular to the direction of energy transfer. If a transverse wave is moving in the positive x-direction, its oscillations are in up and down directions That lie in the y-z plane. If a transverse wave move in the positive x-direction, oscillating above and downward direction lies in the field of Zy.

If you anchor one end of a ribbon or string and hold the other end in your hand, Can you create transverse waves by moving your hand up-and-down menus. If you anchor one end of ribbon or string and hold the other end in your hand, you can create a transverse wave by moving your hand up and down. Notice though, that you Can Also launched waves by moving your hand side-to-side. Note also, that you can also start the wave by moving your hands to the sides. This is an Important point. This is an important point. There are two independent directions in Which wave motion cans occur. There are two independent directions in which wave motion can occur. In this case, These are the y and z directions mentioned above. In this case, this is y and z directions mentioned above. Further, if you carefully move your hand in a clockwise circle, you will from launch waves That DESCRIBE a left-Handed helix propagate away as they want. Furthermore, if you carefully move your hands in a circle clockwise, you will start left-handed helical waves that describe when they spread out. Similarly, if you move your hand in a counter-clockwise circle, a Right-Handed helix will of the form. Similarly, if you move your hands in a circle counter-clockwise, a right hand helix will be formed. These phenomena of simultaneous motion in two directions to go beyond the kinds of waves Can you create on-the surface of water; in general a wave on a string Can be two-dimensional. This phenomenon is simultaneous movement in two directions beyond the type of waves you can make on the surface of the water, generally the waves on a string can be two-dimensional. Two-dimensional transverse waves exhibit a Phenomenon Called Polarization. -Two-dimensional transverse wave shows that the phenomenon is called polarization. A wave Produced by moving your hand in a line, up and down for instance, is a linearly polarized wave, a special case. Waves generated by moving your hands in a row, top and bottom for example, is a linear polarized wave, a special case. A wave Produced by moving your hand in a circle is a circularly polarized wave, another special case. Waves generated by moving your hands in a circle is a circularly polarized wave, one special case. If your motion is not strictly in a line or a circle of your hand will from DESCRIBE of the Ellipse and the will of some elliptically polarized wave. If your motion is not strictly in line or circle your hand will describe an ellipse and the wave will be elliptically polarized.

Electromagnetic waves behave in this Same way, although it is harder to see. electromagnetic waves behave in a similar manner, although more difficult to see. Also electromagnetic waves are transverse two-dimensional waves. Electromagnetic waves are also two-dimensional transverse wave.

Ray theory does not DESCRIBE phenomena Poor 'Interference and Diffraction, Which Require wave theory (involving the phase of the wave). Ray theory does not describe phenomena such as interference and diffraction, which requires the wave theory (involving the phase of the wave). Can you think of a ray of light, in optics, as an idealized narrow beam of electromagnetic radiation. You can think of a ray of light, optics, as an ideal narrow beam of electromagnetic radiation. Rays Are Used to model the propagation of light through an optical system, by Dividing the real light field up into discrete rays That Can be computationally propagated through the system by the techniques of ray tracing. [1] A light ray is a line or curve That is perpendicular to the light's wavefronts (and is therefore collinear with the wave vector). Rays are used to model the propagation of light through an optical system, by dividing the field of real ray of light into discrete computing that can spread through the system with ray tracing techniques. [1] A ray of light is a line or curve that is perpendicular to the wave front of light (and therefore collinear with the wave vector). Light rays bend at the interface Between two dissimilar media Curved and May be in a medium in Which the refractive index changes. Light rays bend at the interface between two different media and can be curved in a medium where the refractive index changes. Geometrical optics describes how rays propagate through an optical system. [1] describes how the geometric optical rays propagating through optical systems. [1]

This two-dimensional nature Should not be confused with the two components of an electromagnetic wave, the electric and magnetic field components, Which are the electromagnetic wave shown in the diagram here. This two-dimensional nature is not to be confused with the two components of electromagnetic waves, electric and magnetic field components, shown in the diagram of electromagnetic waves here. The diagram shows a linear light wave Polarization. The diagram shows the linear polarization of light waves. Each of These fields, the electric and the magnetic, exhibits two-dimensional transverse wave behavior, just like the waves on a string. Each of these fields, and electrical, magnetic behavior shows a two-dimensional transverse waves, like waves on a string.

The transverse plane wave animation Also shown is an example of Linear Polarization. Plane transverse wave animation shown is also an example of linear polarization. The wave shown Could occur on a water surface. Waves shown in surface water can occur.

Transverse waves are waves That are moving perpendicular to the direction of vibration. Transverse waves are waves that move perpendicular to the direction of vibration.

Examples of transverse waves include seismic S (secondary) waves, and motion of electric (E) and magnetic (M) Field in the field of electromagnetic waves, both of which oscillate perpendicular to each other and the direction of energy transfer. Therefore an electromagnetic wave consists of two transverse waves, visible light being an example of an electromagnetic wave. Therefore, the electromagnetic wave comprises two transverse waves, visible light as an example of electromagnetic waves. See electromagnetic spectrum for information on Different types of electromagnetic waves. See electromagnetic spectrum for information on various types of electromagnetic waves.

An oscillating string is another example of a transverse wave; a more everyday example would be an audience wave. An oscillating string is another example of a transverse wave, an example of a more day-to-day will be the wave of the audience.

* Wave speed (v) - the speed of the wave's propagation speed of wave (v) - velocity of wave propagation * Amplitude (A) - the maximum magnitude of the displacement from equilibrium, in SI units of meters. amplitude (A) - the maximum amount of displacement from equilibrium, in SI units of meters. The amplitude is digit in blue in the picture. amplitudes are marked in blue in the picture. * Period (T) - is the time for one wave cycle (two pulses, or from crest to crest or trough to trough), in SI units of seconds (though it May be Referred to as "seconds per cycle"). period (T) - is the time for one wave cycle (two pulses, or from peak to peak or trough to trough), in SI units seconds (though it may be referred to as "cycles per second"). * Frequency (f) - the number of cycles in a unit of time. frequency (f) - the number of cycles in a single unit of time. The SI unit of frequncy is the hertz (Hz) and frequncy SI unit is the hertz (Hz) and

1 Hz = 1 cycle / s = 1 s -1 1 Hz = 1 cycle / s = 1 s -1

* Angular frequency (omega) - is 2pi times the frequency, in SI units of radians per second. angular frequency (omega) - is 2pi times the frequency, in SI units radians per second. * Wavelength (lambda) - The Distance Between any two points at corresponding positions on successive repetitions in the wave, so (for example) from one crest or trough to the next, in SI units of meters. wavelength (lambda) - the distance between two points on the relevant positions at consecutive repetition of the waves, so that (for example) from one peak or trough to the next, in SI units of meters. The wavelength is digit in red in the picture. Wavelength is shown in red in the picture. * Wave number (k) - Also Called the propagation constant, this useful quantity is defined as 2 pi divided by the wavelength, so the SI units are radians per meter. wave number (k) - also called the propagation constant, it's useful quantity is defined as 2 pi divided by the wavelength, so that SI units are radians per meter. * Pulse - one half-wavelength, pulse back from equilibrium - one half wavelength, the equilibrium return

Some useful equations in defining the above Quantities are: Some of the equations is useful in determining the amount of the above is:

v = lambda / T = Fy lambda = lambda / T = lambda f

omega = 2 pi f = 2 pi / T omega = 2 pi f = 2 pi / T

T = 1 / f = 2 pi / omega T = 1 / f = 2 pi / omega

k = 2 pi / omega k = 2 pi / omega

omega = omega = vK vK

The vertical position of a point on the wave, y, can be found as a function of the horizontal position, x, and the time, t, Pls We look at it. Vertical position of a point on the wave, y, can be found as a function of horizontal position, x, and time, t, when we see it. We thank the kind mathematicians for doing this work for us, and obtain the useful equations to DESCRIBE Following the wave motion: We thank the mathematician types to do this job for us, and obtain the following useful equation to describe wave motion:

The Wave Equation Wave Equation One final feature of the wave function That is applying calculus to take the second derivative yields the wave equation, Which is an intriguing and useful Sometimes product (which, once again, We Will thank the mathematicians for and accept without proving it): One of the final feature of the wave function is that the calculus applies to take the second derivative wave equation, which is sometimes useful and interesting products (which, again, we would be grateful to the mathematicians to and accept without proving it):

The second derivative of y with respect to x is equivalent to the second derivative of y with respect to t divided by the wave speed squared. The second derivative of y with respect to x is equal to the second derivative of y with respect to t divided by the square of the wave velocity. The key usefulness of this equation is That Whenever it occurs, We Know That the function y acts as a wave with wave speed v and, therefore, the situation Can be described using the wave function. The main usefulness of this equation is that every time it happens, we know that y acts as a wave function with wave velocity v, and therefore, the situation can be described by using wave functions.